Related papers: Controlling Escape in the Standard Map

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the…

Scanning tunneling microscopy combined with molecular dynamics simulations reveal a dislocation-mediated island diffusion mechanism for Cu on Ag(111), a highly mismatched system. Cluster motion is tracked with atomic precision at multiple…

The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…

We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…

We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…

The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…

We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and H\"older potentials. For small holes, we show that a large class of initial distributions share the…

We argue that at low-energies, typical of the resonance region, the contribution from direct-channel exotic trajectories replaces the Pomeron exchange, typical of high energies. A dual model realizing this idea is suggested. While at high…

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules…

We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak H\"ormander condition where the diffusivity is constant and the…

We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…

Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently.…

While structures and bifurcations controlling tracer particle transport and mixing have been studied extensively for systems with only stretching-and-folding, and to a lesser extent for systems with only cutting-and-shuffling, few studies…

This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…

We investigate exit times from domains of attraction for the motion of a self-stabilized particle traveling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of…

We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we could…

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the…

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…

In this paper, we show that the destruction of the main KAM islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the…